Professor Morris Puzzle #8

Created by Doug Williams
Artwork by Rob Mullarvey

A Professor Morris Puzzle is more than the problem you see. Solving the problem is the starting point for further discussion and investigation. Notes are provided to support that process.

Topics
Multiplication, commutative law

Task Centre Connection
Task 9: Row Points
Task 17: Truth Tiles 2
Task 19: Cookie Count
Task 30: Truth Tiles
Task 123: Bob's Buttons
Task 235: Tables for 25

Strategy
Make a model, write an equation

Solution
Puzzle 9 has a similar problem involving five hands, each with four fingers. Clearly the answer to each puzzle is 20. Also the pair of puzzles shows that 4 x 5 = 5 x 4. More importantly the puzzles demonstrate the importance of context, for in these cases 4x5 does not mean the same as 5x4.


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Green Line

Start Talking

  • Can you create another story which could be represented by 4 x 5 or 5 x 4?
  • Can you create another story in which 4 x 5 and 5 x 4 have the same answer, but do not mean the same thing?
  • When you can swap the numbers in an operation and still get the same answer, the operation is called Commutative. Which other operations are commutative?
  • Make up a new equation. Now try to invent a story which could be represented by this equation.
  • Make up a 'some' story like this: There were 'some' dogs in the yard. Four dogs went for a walk. Three dogs were left behind.
    How many dogs were in the yard to start with?
    Can you write an equation that represents this story?
  • Repeat for a 'some' story like this: There were 'some' dogs in the yard. Some dogs went for a walk. Double that number stayed behind. The total number of dogs was less than 20.
    How many dogs might there have been altogether?
    How many might have gone walking?
  • Make a class book of these stories?